Critical phenomena and Fisher renormalization

Abstract

This thesis offers a full background to the subject of phase transitions and critical phenomena through derivation and explanation of all relevant thermodynamic quantities, and the critical exponents and amplitudes that accompany them. Then, all universal quantities for ferromagnetic phase transition systems including scaling relations and amplitude relations are derived. Two paradigms of phase transition modeling - the one-dimensional and mean field Ising models - are fully evaluated. With a full background in place focus then turns to Fisher renormalization, where the critical exponents and amplitudes of a real system operating under constraint are derived from the ideal system. These exponents and amplitudes are then tested for involution, resulting in a discovery regarding the involutory nature of universal quantities that are fisher renormalized.

Date of Award	2010
Original language	English
Awarding Institution	Coventry University